The 24 Solar Terms

3.1.1Prehistory to the Shang and Zhou: setting up a pole to measure shadows

What a solar term records, at bottom, is the sun's motion over the course of a year, observed directly. The earliest way of observing it was utterly plain:

Set a pole upright in the ground and measure the length of its shadow at noon each day. The day of the longest shadow is the Winter Solstice; the shortest shadow marks the Summer Solstice.

This is the method known as measuring the shadow of an upright pole (the earth-gnomon method, tu gui ce ying). The principle is that in the northern hemisphere the sun's altitude at noon changes with the season: at the Winter Solstice the sun is at its lowest and the shadow is longest, and at the Summer Solstice it is at its highest and the shadow is shortest.

Archaeological evidence:

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  The Taosi site in Shanxi (c. 2100 BCE) has yielded an ancient observatory, in which thirteen rammed-earth pillars formed sighting gaps; the direction of sunrise through them could be used to identify the solar terms. It is regarded as one of the earliest observatories in the world.

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  The Dengfeng observatory in Henan — rebuilt in the Yuan dynasty on the site of the Duke of Zhou's shadow-measuring platform — preserves a complete complex of shadow-measuring structures.

Textual evidence:

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  The Book of Documents, “Canon of Yao” (Yao Dian): “The day is of medium length and the star is Niao; thus fix mid-spring. The day is long and the star is Huo; thus fix mid-summer. The night is of medium length and the star is Xu; thus fix mid-autumn. The day is short and the star is Mao; thus fix mid-winter.” The passage records the use of the four mid-season culminating stars — the star crossing the southern meridian at dusk — to determine the two equinoxes and the two solstices. This is the earliest embryo of the solar terms, with only four nodes.

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  The Rites of Zhou, “Officers of the Earth” (Di Guan): “The shadow at the solstice is one foot five inches.”

3.1.2The Spring and Autumn and Warring States periods: from four nodes to eight

The Zuo Zhuan (Zuo Commentary) and the Guoyu (Discourses of the States) already record eight solar terms grouped as fen, zhi, qi and bi — the equinoxes, the solstices, the openings and the closings:

The Lüshi Chunqiu (Master Lü's Spring and Autumn Annals), “Twelve Records” (Shi Er Ji) — completed in 239 BCE — opens each of its twelve records with a systematic account of the month's celestial signs, phenological phenomena and government ordinances. Eight term names appear explicitly: Start of Spring (Lichun), the equinox (Spring Equinox), Start of Summer (Lixia), the longest day (Summer Solstice), Start of Autumn (Liqiu), the equinox (Autumn Equinox), Start of Winter (Lidong) and the shortest day (Winter Solstice), each with its own description of seasonal phenomena.

3.1.3The Qin and Han: the 24 terms are named and enter the calendar

The Huainanzi, “Astronomical Treatise” (Tian Wen Xun) (c. 139 BCE) — the first place where the names of all 24 solar terms appear complete:

“The sun moves one degree a day; fifteen days make one term, and from this arise the changes of the twenty-four periods. When the Dipper points to Zi it is the Winter Solstice… fifteen days later it points to Gui, and it is Minor Cold; fifteen days after that it points to Chou, and it is Major Cold…”

The Huainanzi gives the full set of 24 solar term names, in an order exactly the same as the modern one. Its author was Liu An, King of Huainan (179–122 BCE), with his retainers, the “Eight Gentlemen of Huainan”.

The Zhoubi Suanjing (the Gnomon of the Zhou) (c. 1st century BCE) gives a method of computing the terms from “gnomon shadow lengths” and appends a table of shadow lengths for all 24 terms. It is one of China's earliest works of mathematical astronomy.

Emperor Wu of Han's Taichu Calendar (Tai Chu Li) (104 BCE) — the 24 Solar Terms formally entered the state calendar. The achievement belongs to Luoxia Hong and his colleagues.

The key change: from the mean term to the fixed term

Because the Earth's orbit is an ellipse, the sun's apparent motion is not uniform — faster at perihelion, slower at aphelion — so under the fixed-term method the interval between terms ranges from 14.7 to 15.7 days. This was the decisive step in raising the precision.

3.1.4Yuan, Ming and Qing: peak precision and the meeting of East and West

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  The Shoushi Calendar of the Yuan: Guo Shoujing computed the sun's position by the “method of differences”, bringing the calculation of the terms to an exceptionally high standard of accuracy.

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  The Datong Calendar of the Ming: it continued the Shoushi Calendar but went unrevised for so long that its errors accumulated.

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  The Shixian Calendar of the early Qing (1645): Johann Adam Schall von Bell directed the change to the fixed-term method — the last major technical reform in the history of the 24 solar terms.

3.1.5The present day: confirmation twice over, from heritage listing and from a national standard

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  On Nov 30, 2016, UNESCO inscribed “the 24 Solar Terms — the knowledge of time and the practices developed in China through observation of the sun's annual motion” on the Representative List of the Intangible Cultural Heritage of Humanity.

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  In 2017 the national standard Calculation and Promulgation of the Lunar Calendar (GB/T 33661-2017) was published, laying down exactly how the solar terms are to be computed.

3.2.1What solar longitude is

The ecliptic: the path the sun appears to trace across the celestial sphere (in fact the projection of the Earth's orbit onto that sphere). Solar longitude (λ): the angle giving the sun's position on the ecliptic, measured eastward from the spring equinox point, 0°–360°.

Definition: each additional 15° of solar longitude marks one solar term.

3.2.2The four key nodes

In antiquity the Winter Solstice was the most important festival of the year. It is the day on which “yang energy begins to grow”, and the Zhou dynasty at one time took the month containing it — the month of Zi — as the first month of the year. The Book of the Later Han records: “Around the Winter Solstice the gentleman settles his body and quiets himself, and all officials cease their business.” There is a popular saying that “the Winter Solstice is as great as the New Year”.

3.2.3How the fixed-term and mean-term methods differ

Why this matters: because the fixed-term method makes the date of a term drift, the exact moment at which a term begins must be known to the day, even to the hour. This is why, when a Bazi chart is cast, a birth only a few hours away from that moment can still change the Month Pillar.

3.3.1Spring

The three pentads of spring

3.3.2Summer

The three pentads of summer

3.3.3Autumn

The three pentads of autumn

3.3.4Winter

The three pentads of winter

3.3.5The pentad system and the 72 pentads

Each solar term is divided into “three pentads”, each pentad five days, giving 24 × 3 = 72 pentads in the year.

A complete system: phenological change was recorded with five days as the smallest unit — a systematic contribution by early Chinese observers to phenology. The content of the 72 pentads is preserved mainly in the Yueling Qishier Hou Jijie (Collected Explanations of the 72 Pentads of the Monthly Ordinances) by Wu Cheng of the Yuan dynasty.

Three kinds of phenological content:

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  Plant signs: peach trees come into blossom, plants and trees sprout, the paulownia blossoms, the chrysanthemum shows yellow, plants and trees turn yellow and shed

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  Animal signs: hibernating insects begin to stir, the oriole sings, the wild geese come, hawks make offerings of birds, tigers begin to mate

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  Weather and water signs: the east wind thaws the ice, thunder sounds, rainbows first appear, water begins to freeze, the springs begin to move

Scientific value: the 72 pentads are in effect a system of biological and climatic observation indicators, running along the same lines as “phenological observation” in modern agricultural meteorology. China's phenological tradition is more than a thousand years older than Europe's — Linnaeus set up a phenological observation network in Sweden in 1736.

3.4.1The twelve sectional terms and the twelve median terms

The 24 solar terms fall strictly into two groups:

How they are allotted:

The rule: counting from the month that contains the Winter Solstice, the odd-numbered terms are sectional and the even-numbered ones median — Winter Solstice (median), Minor Cold (sectional), Major Cold (median), Start of Spring (sectional)… alternating all the way.

A mnemonic: “Li, Jing, Qing, Li, Mang; Xiao, Li, Bai, Han, Li; Da Xue, Xiao Han” — the opening syllables of the twelve sectional terms in order, with the median terms in between left out.

3.4.2Placing the leap month where there is no median term

The rule: if a lunar month contains no median term, that month is a leap month.

Why this works:

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  One synodic month is about 29.53 days

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  The average interval between two median terms is about 30.44 days

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  Since 30.44 is greater than 29.53, some months are bound to “miss” the median term

An example: in 2023 the Lunar Calendar had a leap second month, because that month contained no median term.

How the method developed:

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  The Taichu Calendar used this method from the outset

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  Earlier ages, however, also used a “leap cycle” — seven leap months in nineteen years, for instance — inserting the leap month by accumulated time difference, so that it did not always fall in a month without a median term

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  The Shixian Calendar of the Qing then applied the “leap month without a median term” rule strictly

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  The modern national standard GB/T 33661-2017 states explicitly that a month containing no median term is a leap month

An important note: a leap month has no effect on casting a Bazi chart. The Month Pillar is settled entirely by the sectional terms; a leap month in the Lunar Calendar is only a device for keeping the calendar in step.

3.5.1Where the Month Pillar begins and ends

In Bazi, a “month” is a sectional-term month, not a lunar month.

An example:

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  In 2024 the Start of Spring fell on Feb 4 at 16:27

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  A birth at 10:00 on Feb 4 → the Month Pillar still falls in the Chou Month (the twelfth month of the previous year)

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  A birth at 20:00 on Feb 4 → the Month Pillar falls in the Yin Month (the first month of that year)

This is why the moment a term begins must be known to the minute.

3.5.2The strength of the Five Elements and Adjustment

The Month Command decides which element is “in command” (see Chapter 02, §2.3.3):

The core logic of Adjustment: a solar term stands for a “climate”, and the climate decides whether a chart is cold or warm, dry or damp — and therefore what is needed to balance it.

3.5.3The handover of Major Luck and the sectional terms

The casting and the changing of Major Luck depend entirely on the sectional terms:

Forward sequence: birth date → days to the next sectional term ÷ 3 = the starting age
Backward sequence: birth date → days back to the previous sectional term ÷ 3 = the starting age

The moment of “handover”: the day on which one period of Major Luck gives way to the next is treated as a turning point in a person's fortune. Traditionally there are various observances about what to do in the days around a handover (the “handing over and shedding” of Major Luck).

How sectional terms work within the Annual Fortune: the strength of the Five Elements over a year shifts with the solar terms — after the Start of Autumn, for instance, Metal qi gradually strengthens, and after Frost's Descent, Water qi begins to rise. This is called “the fine-grained action of the Month Command”.

3.5.4Four traditional uses of the solar terms

3.6.1The popular Solar Terms Song

Spring: Start of Spring, Rain Water, Awakening of Insects, Spring Equinox, Pure Brightness, Grain Rain. Summer: Start of Summer, Grain Buds, Grain in Ear, Summer Solstice, Minor Heat, Major Heat. Autumn: Start of Autumn, End of Heat, White Dew, Autumn Equinox, Cold Dew, Frost's Descent. Winter: Start of Winter, Minor Snow, Major Snow, Winter Solstice, Minor Cold, Major Cold. Two terms every month, never changing, no more than a day or two apart. In the first half of the year the 6th and the 21st, in the second half the 8th and the 23rd.

3.6.2Line by line

The first line (spring): Start of Spring, Rain Water, Awakening of Insects, Spring Equinox, Pure Brightness, Grain Rain. The second line (summer): Start of Summer, Grain Buds, Grain in Ear, Summer Solstice, Minor Heat, Major Heat. The third line (autumn): Start of Autumn, End of Heat, White Dew, Autumn Equinox, Cold Dew, Frost's Descent. The fourth line (winter): Start of Winter, Minor Snow, Major Snow, Winter Solstice, Minor Cold, Major Cold.

The last two lines give the dates as a rule of thumb:

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  In the first half of the year the terms fall mostly around the 6th and the 21st of the month (Pure Brightness on 4/5, Grain Rain on 4/20, for example)

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  In the second half they fall mostly around the 8th and the 23rd of the month (Start of Autumn on 8/7, End of Heat on 8/23, for example)

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  This is a rough rule belonging to the mean-term method; under the fixed-term method it is off by a day or two

3.6.3Another way to remember it: the order of the eight nodes

The four Beginnings, the two equinoxes and the two solstices are the eight most important nodes; learn these eight first:

Start of Spring → Spring Equinox → Start of Summer → Summer Solstice → Start of Autumn → Autumn Equinox → Start of Winter → Winter Solstice
  ↑        ↑        ↑        ↑
315°      0°       45°      90°      135°     180°     225°     270°

Insert two more terms between each pair of nodes and you have the complete set of 24 solar terms.

3.7.1Xihe (a legendary figure)

The Book of Documents, “Canon of Yao”, records: “He commanded Xihe, in reverent accord with Heaven above, to compute and delineate the sun, moon and stars, and to deliver the seasons respectfully to the people.” Xihe is described as an official of high antiquity in charge of astronomy and the calendar, divided into four men — Xi Zhong, Xi Shu, He Zhong and He Shu — stationed in the four directions, east, south, west and north, to observe the four mid-season culminating stars and so fix the solar terms.

Cultural significance: Xihe is the mythological archetype of the Chinese astronomical office, and the name later became that of the “goddess who drives the sun” (the Classic of Mountains and Seas (Shan Hai Jing): “Xihe was the wife of Di Jun and bore the ten suns”). The myth reflects how closely the practice of observing the heavens and granting the seasons was bound up with political power in early China — the calendar was a symbol of royal authority.

3.7.2Liu An (179–122 BCE)

Who he was: King of Huainan in the Western Han, grandson of Liu Bang, Emperor Gaozu of Han, and uncle of Emperor Wu.

What he did:

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  He directed the compilation of the Huainanzi (also known as the Huainan Honglie), one of the most important works of philosophy and science in ancient China.

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  The “Astronomical Treatise” (Tian Wen Xun) of the Huainanzi records the names of all 24 solar terms — the single most important piece of documentary evidence in their history.

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  The book also treats Yin-Yang, the Five Elements, celestial phenomena, geography and musical pitch in a systematic way, and it is the great summation of ancient Chinese “cosmology”.

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  He was fond of the technical arts (fangshu) and drew several thousand retainers and practitioners of those arts to his court; when a plot of rebellion came to light, he took his own life.

Scholarly standing: the Huainanzi is the core text that no study of the origin of the 24 solar terms can bypass. Had it been lost, the question of where the solar terms came from would be far more obscure than it is.

3.7.3Wu Cheng (1249–1333)

Who he was: a scholar and Neo-Confucian of the Yuan dynasty, courtesy name Youqing, style name Caolu, a native of Chongren in Fuzhou (present-day Chongren, Jiangxi).

What he did:

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  He rose to the post of Hanlin academician and was one of the most important Neo-Confucian scholars of the Yuan.

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  He wrote the Yueling Qishier Hou Jijie, setting out the complete system of the 72 pentads and glossing each pentad with its astronomical, climatic and phenological basis.

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  It is the most complete surviving document on the 72 pentads and the most important ancient source for the study of phenology today.

Scholarly standing: the Yueling Qishier Hou Jijie is the “standard answer” for the phenological system of the solar terms; every later account of the three pentads derives from it.

3.7.4Guo Shoujing (1231–1316)

See Chapter 01, §1.6.5. In the field of the solar terms his contributions were:

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  He used the “method of differences” (third-order interpolation) to compute the sun's position on the ecliptic precisely, bringing the calculation of the terms to the highest standard of accuracy in the ancient world

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  He obtained measured data at different latitudes through the “four seas survey”, giving the calculation of the terms a solid foundation

3.7.5Xu Guangqi (1562–1633)

Who he was: a scientist and statesman of the Ming dynasty, courtesy name Zixian, style name Xuanhu, a native of Shanghai. He rose to be Minister of Rites and Grand Secretary of the Wenyuan Pavilion.

What he did:

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  He directed the compilation of the Chongzhen Lishu, completed in 1634, which brought the Western astronomical system into China.

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  With Matteo Ricci he translated the first six books of the Elements (Jihe Yuanben), a landmark in scientific exchange between China and the West.

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  He wrote the Complete Treatise on Agriculture (Nong Zheng Quan Shu), a systematic survey of Chinese agricultural technique with long passages on the relation between the solar terms and farm work.

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  He is a representative figure of the “bringing East and West together” current in Chinese scientific thought.

His relation to the solar terms: the Chongzhen Lishu laid the ground for the early Qing Shixian Calendar's adoption of the fixed-term method. One can say that the precise modern definition of the solar terms begins with this reform under Xu Guangqi.

3.7.6Johann Adam Schall von Bell (1592–1666)

See Chapter 01, §1.6.6. His central contribution was the formal adoption of the fixed-term method in the Shixian Calendar, the last major technical reform in the history of the 24 solar terms, and one whose effects are still with us.

3.8.1The solar terms by Solar Calendar month

3.8.2The Earthly Branch and zodiac month of each term